Quantum limited josephson amplifier with spatial separation between spectrally degenerate signal and idler modes

ABSTRACT

A technique relates to a quantum-limited microwave amplifier. A Josephson ring modulator (JRM) is connected to a first lumped-element resonator. The first lumped-element resonator includes one or more first lumped elements. A second lumped-element resonator is connected to the JRM, and the second lumped-element resonator includes one or more second lumped elements. The JRM, the first lumped-element resonator, and the second-lumped element resonator form a Josephson parametric converter (JPC). The one or more first lumped elements and the one or more second lumped elements have a value that is the same, thereby configuring the JPC to be spectrally degenerate.

PRIORITY

This application is a divisional of U.S. Non-Provisional applicationSer. No. 15/278,918, entitled “QUANTUM LIMITED JOSEPHSON AMPLIFIER WITHSPATIAL SEPARATION BETWEEN SPECTRALLY DEGENERATE SIGNAL AND IDLERMODES”, filed Sep. 28, 2016, which is incorporated herein by referencein its entirety.

BACKGROUND

The present invention relates to superconducting electronic devices, andmore specifically, a quantum-limited Josephson amplifier with spatialseparation between spectrally degenerate signal and idler modes.

In circuit quantum electrodynamics, quantum computing employs nonlinearsuperconducting devices called qubits to manipulate and store quantuminformation at microwave frequencies, and resonators (e.g., as atwo-dimensional (2D) planar waveguide or as a three-dimensional (3D)microwave cavity) to read out and facilitate interaction among qubits.As one example, each superconducting qubit can include one or moreJosephson junctions shunted by capacitors in parallel with thejunctions. The qubits are capacitively coupled to resonators (e.g., 2Dor 3D microwave cavities).

SUMMARY

According to one or more embodiments, a quantum-limited microwaveamplifier is provided. The amplifier includes a Josephson ring modulator(JRM), and a first lumped-element resonator connected to the JRM. Thefirst lumped-element resonator includes one or more first lumpedelements. Also, the amplifier includes a second lumped-element resonatorconnected to the JRM. The second lumped-element resonator includes oneor more second lumped elements. The JRM, the first lumped-elementresonator, and the second-lumped element resonator form a Josephsonparametric converter (JPC). The one or more first lumped elements andthe one or more second lumped elements have a value that is the same,thereby configuring the JPC to be spectrally degenerate.

According to one or more embodiments, a method of configuring aquantum-limited microwave amplifier is provided. The method includesproviding a JRM, and providing a first lumped-element resonatorconnected to the JRM, where the first lumped-element resonator includesone or more first lumped elements. Also, the method includes providing asecond lumped-element resonator connected to the JRM, where the secondlumped-element resonator includes one or more second lumped elements.The JRM, the first lumped-element resonator, and the second-lumpedelement resonator form a JPC. The one or more first lumped elements andthe one or more second lumped elements have a value that is the same,thereby configuring the JPC to be spectrally degenerate.

According to one or more embodiments, a system for remotely entanglingqubits via measurement is provided. The system includes a JPC and afirst qubit-resonator system connected to the JPC. The firstqubit-resonator system includes a first qubit coupled to a first readoutresonator. Also, the system includes a second qubit-resonator systemconnected to the JPC. The second qubit-resonator system includes asecond qubit coupled to a second readout resonator, and the JPC isconfigured to remotely entangle the first qubit and the second qubit byreading out both the first and the second readout resonators at thefrequency X.

According to one or more embodiments, a method of configuring a systemfor remotely entangling qubits via measurement is provided. The methodincludes providing a JPC, and providing a first qubit-resonator systemconnected to the JPC. The first qubit-resonator system includes a firstqubit connected to a first readout resonator. Also, the method includesproviding a second qubit-resonator system connected to the JPC, wherethe second qubit-resonator system includes a second qubit connected to asecond readout resonator. The JPC is configured to remotely entangle thefirst qubit and the second qubit by reading out both the first and thesecond readout resonators at the frequency X.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic of a circuit for a superconducting Josephsonparametric converter according to one or more embodiments

FIG. 2 is a schematic of a system for remotely entangling qubits usingthe Josephson parametric converter according to one or more embodiments.

FIG. 3 is a flowchart of a method of configuring a quantum-limitedmicrowave amplifier according to one or more embodiments.

FIG. 4 is a flowchart of a method for configuring a system for remotelyentangling qubits via measurement according to one or more embodiments.

DETAILED DESCRIPTION

Various embodiments are described herein with reference to the relateddrawings. Alternative embodiments can be devised without departing fromthe scope of this document. It is noted that various connections andpositional relationships (e.g., over, below, adjacent, etc.) are setforth between elements in the following description and in the drawings.These connections and/or positional relationships, unless specifiedotherwise, can be direct or indirect, and are not intended to belimiting in this respect. Accordingly, a coupling of entities can referto either a direct or an indirect coupling, and a positionalrelationship between entities can be a direct or indirect positionalrelationship. As an example of an indirect positional relationship,references to forming layer “A” over layer “B” include situations inwhich one or more intermediate layers (e.g., layer “C”) is between layer“A” and layer “B” as long as the relevant characteristics andfunctionalities of layer “A” and layer “B” are not substantially changedby the intermediate layer(s).

The electromagnetic energy associated with the qubit is stored in theJosephson junctions and in the capacitive and inductive elements formingthe qubit. In one example, to read out the qubit state, a microwavesignal is applied to the microwave readout cavity that couples to thequbit at the cavity frequency corresponding to the qubit state. Thetransmitted (or reflected) microwave signal goes through multiplethermal isolation stages and low-noise amplifiers that are required toblock or reduce the noise and improve the signal-to-noise ratio. Themicrowave signal is measured at room temperature. The amplitude and/orphase of the returned/output microwave signal carry information aboutthe qubit state, such as being at the ground or excited states or at asuperposition of the two states. A microwave readout provides a stablesignal amplitude for control, and commercial off-the-shelf (COTS)hardware is available to use that covers most of microwave frequencyranges.

A Josephson ring modulator (JRM) is a nonlinear dispersive element basedon Josephson tunnel junctions that can perform three-wave mixing ofmicrowave signals at the quantum limit. The JRM consists of fournominally identical Josephson junctions (JJ) arranged in a Wheatstonebridge configuration. In order to construct a nondegenerate parametricdevice such as a Josephson parametric converter (JPC), which is capableof amplifying and/or mixing microwave signals at the quantum limit, theJRM is incorporated into two microwave resonators at an RF-currentanti-node of their fundamental eigenmodes. As has been demonstrated inseveral experimental and theoretical works, the performances of theseJPCs, namely power gain, dynamical bandwidth, and dynamic range, arestrongly dependent on the critical current of the JJs of the JRM, thespecific realization of the electromagnetic environment (i.e., themicrowave resonators), and the coupling between the JRM and theresonators.

In order to enhance certain performances of JPCs, various microwaveresonators have been realized and proposed, such as, coplanar striplineresonators, microstrip resonators, compact/lumped-element resonators,and three-dimensional cavities. In the state-of-the-art, it has alsobeen suggested to enhance the dynamic range of JPCs by enhancing thecritical current of JJs that form the JRM by, for example, using niobiumjunctions and nanobridges. Moreover, it has been shown that the tunablebandwidth of JPCs can be increased by shunting the JJs of the JRM withlinear inductance.

Josephson parametric converters are quantum-limited microwave amplifiersthat can be used to readout the quantum state of superconducting qubits,quantum dots, etc. The JPC is a nondegenerate amplifier in which thesignal and idler modes are both spatially and spectrally separate. Thesignal and idler have different physical ports and resonators (i.e.,spatial separation), and the signal and idler also have differentfrequencies (i.e., spectral separation).

The Josephson parametric amplifier (JPA) is a degenerate amplifier inwhich the signal and idler modes share the same physical port andresonator, but can have either slightly different frequencies within thebandwidth of the amplifier (i.e., phase preserving mode) or have thesame frequency (i.e., phase sensitive mode).

The same applies for Josephson Traveling Wave Parametric Amplifiers(JTWPAs) and Kinetic Inductance Traveling Wave Amplifiers (KITWA) whichare formed using nonlinear transmission lines that lack resonators(except those used within the transmission lines for phase matchingpurposes).

However, in the-state-of-the-art, there is no quantum-limited parametricamplifier available that has different physical ports for the signal andidler modes while allowing their frequencies to match, i.e., allowingthe signal and idler frequencies to match. One main reason is that bymaking the JPC microstrip resonators (transmission-line based)identical, the pump frequency required for amplification whichcorresponds to the sum of the signal and idler resonance frequencieswould coincide with the frequency of the second harmonic of the signaland idler resonators, thus making the “pump drive soft” which negativelyaffects the amplifier performance. Furthermore, by making the twotransmission-line resonators identical (i.e., making the signal andidler resonators identical) for the signal and idler modes, thefrequency of the “parasitic” common mode of the device (whichcorresponds to direct transmission between the signal and idler ports)would coincide with the signal and idler frequencies as well leading todirect leakage between the ports (i.e., between the signal and idlerports).

Turning now to an overview of aspects of the present invention, one ormore embodiments discuss how to build or configure a quantum limitedmicrowave amplifier that is spatially nondegenerate (i.e., has differentports for the signal and idler modes), is spectrally degenerate (i.e.,has the same frequency for the signal and idler resonators), and is ableperform three-wave mixing. In order to achieve this, one or moreembodiments utilize lumped-element JPCs whose the signal and idlerresonators are made of lumped-element inductors and capacitors, andthese lumped-elements for the signal and idler resonators are nominallyidentical. The combination of the two requirements constitutes a benefitin the JPC. One or more embodiments illustrate that such a structure ordevice configuration would addresses the problems outlined previouslywith regard to JPCs that are based on transmission-line resonators. Thefact that the lumped-element resonators lack a second harmonic resonancemode (i.e., at twice the fundamental resonance frequency) ensures thatthe pump drive remains “stiff” in embodiments, thus maintaining thedevice performance compared to the nondegenerate case. Furthermore, inone or more embodiments, the frequency of the common mode of thelumped-element JPC does not coincide with the frequency of signal andidler modes (e.g., the frequency of the common mode is either higher orlower than the frequency of the signal or the idler, depending on theexact circuit), thus ensuring the two modes (signal and idler) areisolated against direct transmission across the signal and idler ports.This means that the common mode is not equal to the resonance frequencyof the signal or the idler resonator.

Turning now to a more detailed description of aspects of the presentinvention, FIG. 1 is a schematic of a circuit for a JPC 100 according toone or more embodiments. The JPC 100 includes port 150A and port 150B.The port 150A can be connected to a broadband 180 degree hybrid coupler120A and the port 150B can be connected to a broadband 180 degree hybridcoupler 120B. The 180 degree hybrid couplers 120A and 120B each have adifference (Δ) port and a sum (Σ) port. For 180 degree hybrid coupler120A, the idler (I) is connected to the Δ port and the pump (P) isconnected to the Σ port. For 180 degree hybrid coupler 120B, the signal(S) is connected to the Δ port and a termination impendence point (e.g.,50 ohm (Ω) termination environment) is connected to the Σ port.

A 180° hybrid coupler is a 4-port microwave device that is reciprocal,matched, and ideally lossless. The 180° hybrid splits an input signalinto two equal amplitude outputs. When fed from its sum port (Σ) the180° hybrid provides two equal-amplitude in-phase output signals.Whereas when fed from its difference port (Δ), it provides two equalamplitude 180° out-of-phase output signals.

The JPC 100 includes a multi-Josephson junction ring modulator (MJRM)110. The MJRM 110 includes multiple Josephson junctions 130 connectedtogether (in series) to form the loop/ring in the MJRM 110. The MJRM 110includes an array of N Josephson junctions 130. In one implementation,N=1-15 in the array of N JJs. In one implementation, N=6 JJs in the MRJM110. As understood by one skilled in the art, a magnetic flux Φ threadsthe loop of the MJRM 110. The choice of the number of Josephsonjunctions N in each arm of the JRM can be influenced by two conflictingconsiderations and the balance between them. The first consideration isto enhance the dynamic range of the device by adding more Josephsonjunctions in series, while the second is not to dilute the nonlinearityof the JRM considerably (since the nonlinearity of the JRM decreaseswith increasing N).

An idler resonator 161 includes lumped-element capacitors 10A and 10B inparallel with the MJRM 110. A signal resonator 162 includeslumped-elements capacitors 10C and 10D in parallel with the MJRM 110.The idler resonator 161 and the signal resonator 162 both share orutilize the MJRM 110. In both the idler resonator 161 and the signalresonator 162, the value is the same for each of the lumped-elementcapacitors 10A, 10B, 10C, and 10D and this value is designated as 2C,where C represents capacitance. Although lumped-element capacitors 10A-Dare illustrated, one implementation can have in addition lumped-elementinductors in parallel or series with the MJRM 110. A microwavecomponent/element is described as lumped (versus distributed) if itsdimensions are very small compared to the wavelength of the minimumworking frequency (e.g., smaller than 1/10 of the wavelengthcorresponding to the minimum operational frequency of the device). Forexample, Josephson junctions are considered to a very goodapproximation, as lumped nonlinear inductors for microwave signals inthe range 1-20 GHz.

The lumped-element capacitors 10A and 10B of the idler resonator 161connect to opposite ends of the MJRM 110, for example, at nodes 50A and50B of the MJRM 110. The lumped-element capacitors 10C and 10D of thesignal resonator 162 connect to opposite ends of the MJRM 110, forexample, at nodes 50C and 50D of the MJRM 110.

The JPC 100 includes coupling capacitors 20A and 20B which connect theport 150A to the idler resonator 161. Also, the JPC includes couplingcapacitors 20C and 20D which connect the port 150B to the signalresonator 162. The coupling capacitors 20A, 20B, 20C, and 20D each havethe same value, and this value is designated C_(c)/2. The value ofcoupling capacitors 20A, 20B, 20C, and 20D is mainly determined suchthat it sets a desirable bandwidth for the idler resonator 161 and thesignal resonator 162 (without sacrificing the device stability as wouldbe understood by one skilled in the art).

The idler microwave signal/tone 151 is at the frequency f_(I) and thesignal microwave signal/tone 152 is at the frequency f_(S). The pumpmicrowave signal/tone 153 is at the frequency f_(P). For the JPC device100 to be in amplification mode (with photon gain), the applied pumpfrequency f_(P) satisfies the relationf _(P) =f _(I) +f _(S),

where f_(S) and f_(I) are the frequency of the Signal (S) and the Idler(I) tones respectively.

In a state-of-the-art JPC, the idler microwave signal and the signalmicrowave signal are required to satisfy the requirement of f_(S)<f_(I).For example, the idler frequency f_(I) can be 10 gigahertz (GHz) and thesignal frequency f_(S) can be 7 GHz, resulting in the pump frequencyf_(P) being 17 GHz. In the state-of-the-art JPC, the idler frequencyf_(I) cannot be equal (or nearly equal) to the signal frequency f_(S)because the pump frequency f_(P) (where f_(P)=f_(I)+f_(S)) wouldcoincide with the second harmonic of the idler resonator and the signalresonator, thus making the pump drive soft and negatively affecting theamplifier performance, such as significantly decreasing its dynamicrange (where the dynamic range is the maximum input power that thedevice can handle at a certain working point).

In contrast to the state-of-the-art, the JPC 100 in embodiments has thelumped-element idler resonator 161 and lumped-element signal resonator162, and the idler and signal resonators 161 and 162 do not have asecond harmonic which ensures that the pump drive remains stiff, thusmaintaining the JPC performance compared to the nondegenerate case (inthe state-of-the-art). Therefore, in the JPC 100, the idler microwavesignal 151 at frequency f_(I) and the signal microwave signal 152 atfrequency f_(S) are configured to satisfy the relationf_(I)=f_(S).

Therefore, the idler frequency f_(I) is to be equal (or about equal) tothe signal frequency f_(S). For example, the idler frequency f_(I) canbe 10 gigahertz (GHz) and the signal frequency f_(S) can be 10 GHz,resulting in the pump frequency f_(P) being 20 GHz. The frequency of thepump drive f_(P) (in amplification) of the lumped-element JPC 100 doesnot coincide with the frequency (which is the same) of signal and idlermodes (resonators 162 and 161) and/or does not coincide with the secondresonance frequency of the lumped-element resonators which are the idlerresonator 161 and the signal resonator 162. Also, the frequency of thecommon mode of the JPC device 100 does not coincide with f_(I) andf_(S). It is either higher or lower than the f_(I) and f_(S), therebyensuring that the idler mode (idler resonator 161) and signal mode(signal resonator 162) are isolated against direct transmission acrossthe signal port (i.e., Δ port of the hybrid coupler 120B) and idler port(i.e., Δ port of the hybrid coupler 120A). That is, the idler microwavesignal 151 (input at the Δ (idler) port of the hybrid coupler 120A) isnot output at the Δ (signal) port of the hybrid coupler 120B, and thesignal microwave signal 152 (input at the Δ (signal) port the hybridcoupler 120B) is not output at the Δ (idler) port of the hybrid coupler120A, even while satisfying the condition f_(I)=f_(S).

The JPC 100 including the capacitors 10A-D and 20A-D (with the exceptionof the dielectric material in the capacitors), transmission lines 30,Josephson junctions 130 (with the exception of the thin insulatingmaterial), and ports 150A and 150B are made of superconducting material.Additionally, the hybrid couplers 120A and 120B are made of low lossnormal metals or can be made of superconducting material. Also, thequbit-resonator systems discussed below are made of superconductingmaterial. Examples of superconducting materials (at low temperatures,such as about 10-100 millikelvin (mK), or about 4 K) include niobium,aluminum, tantalum, etc.

FIG. 2 is a schematic of a system 200 for remotely entangling qubitsusing the JPC 100 according to one or more embodiments. In FIG. 2, thedetails of the JPC 100 are omitted for the sake of clarity, and it isunderstood that the JPC 100 includes the features discussed in FIG. 1.The system 200 illustrates the JPC 100 connected to qubit-resonatorsystem 220A via the idler port 150A through hybrid coupler 120A and theJPC 100 connected to qubit-resonator system 220B via the signal port150B through hybrid coupler 120B.

The qubit-resonator system 220A includes qubit 205A connected to itsreadout resonator 210A. The qubit-resonator system 220B includes qubit205B connected to its readout resonator 210B.

In one implementation, the qubit-resonator systems 220A and 220B can becoupled to each other locally on the same chip. In anotherimplementation, qubit-resonator systems 220A and 220B can be remote fromeach other on the same chip or on two different chips. The readoutresonators 210A and 210B are configured to have the same resonancefrequency X which coincides with the two resonance frequencies of theJPC (i.e., the signal resonator 162 and the idler resonator 161). Inother words, the readout resonators 210A and 210B, the idler resonator161, and the signal resonator 162 each have the same resonance frequencyX. It is noted that the frequency X represents a microwave frequencysuch, for example, 10 GHz. It is appreciated that the frequency X can beother microwave frequencies. As noted above, since the idler resonator161 and the signal resonator 162 are lumped-element resonators, theidler resonator 161 and signal resonator 162 only have a fundamentalresonance frequency which is a first resonance frequency and do not havea second resonance frequency at twice the fundamental resonancefrequency, thereby allowing the idler resonator 161 and signal resonator162 to have the same resonance frequency and allowing the JPC 100 tooperate as an amplifier f_(P)=f_(I)+f_(S) without negative effects, suchas a reduction in the dynamic range of the devices and direct powerleakage between the signal and idler resonators and ports.

In qubit-resonator systems 220A and 220B, the respective qubits 205A and205B can have two different qubit frequencies in one implementation. Inanother implementation, the qubits 205A and 205B can have the same qubitfrequency.

In qubit-resonator system 220A, the qubit 205A can be driven separatelythrough a separate port not necessarily through its correspondingreadout resonator 210A. In qubit-resonator systems 220B, the qubit 205Bcan be driven separately through a separate port not necessarily throughits corresponding readout resonator 210B.

The JPC 100 when operated in amplification (meaning f_(P)=f_(I)+f_(S))can remotely entangle (at the same frequency X) these two qubits 205Aand 205B by generating and sending to the readout resonators 210A and210B two readout tones/signals (i.e., microwave signals 151′ and 152′,respectively). The microwave signal 151′ at frequency f_(I) andmicrowave signal 152′ at frequency f_(S) each include entangled photons(signal and idler), and both microwave signals 151′ and 152′ are atfrequency X, which means f_(I)=f_(S)=frequency X. The microwave signals151′ and 152′ are readout signals that respectively measure the qubits205A and 205B by individually probing (i.e., reading out) their readoutresonators 210A and 210B.

The qubits 205A and 205B are initialized to a certain state or driven toa certain state as a result of a calculation. The entanglement happensas a result of joint measurement of the two qubit states of qubits 205Aand 205B using the two entangled microwave signals 151′ and 152′(readout tones) which include entangled photons. In other words, probingthe state of the two qubits 205A and 205B with two entangled readoutbeams (microwave signals 151′ and 152′) results in entanglement of thetwo qubits 205A and 205B.

An example scenario is provided for illustration and not limitation. Themicrowave signal 151 at frequency f_(I) (equal to frequency X) istransmitted to the JPC 100 via the difference port of hybrid coupler120A through port 150A of the JPC 100. The microwave signal 152 atfrequency f_(S) (also equal to frequency X) is transmitted to the JPC100 via the difference port of hybrid coupler 120B through port 150B ofthe JPC 100. Additionally, the pump microwave signal 153 is applied viathe sum port of the hybrid coupler 120A through the port 150A, and thepump microwave signal 153 is at the pump frequency f_(P)=f_(I)+f_(S).

The microwave signal 151 interacts with the idler resonator 161 whichincludes interacting with the MJRM 110, while the microwave signal 152interacts with the signal resonator 162 which also includes interactingwith the MJRM 110. By both microwave signals 151 and 152 togetherinteracting with the MJRM 110, the photons of microwave signal 151become entangled with the photons of microwave signal 152 (and viceversa) via a three-wave mixing process taking place in the JPC device100 (or in other words, through a down-conversion of pump photons intoentangled pairs of signal and idler photons). After interacting with theidler resonator 161 (including MJRM 110), the reflected/generatedmicrowave signal 151 is designated as microwave signal 151′. Likewise,after interacting with the signal resonator 162 (including MJRM 110),the reflected/generated microwave signal 152 is designated as microwavesignal 152′. The reflected microwave signal 151′ and 152′ have entangledphotons at the frequency f_(I)=f_(S)=frequency X (e.g., 10 GHz). Forexample, there can be a first pair of entangled photons, e.g., onephoton in the microwave signal 151′ is entangled with one photon in themicrowave signal 152′, a second pair of entangled photons, e.g., anotherphoton in the microwave signal 151′ is entangled with another photon inthe microwave signal 152′, through a last pair of entangled photons,e.g., yet another photon in the microwave signal 151′ is entangled withyet another photon in the microwave signal 152′. Accordingly, there canbe multiple pairs of entangled photons between the microwave signal 151′and 152′.

The reflected microwave signal 151′ is transmitted to thequbit-resonator system 220A as the readout signal for readout resonator210A while the reflected microwave signal 152′ is transmitted to thequbit-resonator system 220B as the readout signal for readout resonator210B, thereby entangling the qubits 205A and 205B. To measure qubit205A, the microwave signal 151′ at frequency X causes the readoutresonator 210A to read out the state information of qubit 205A, and thismicrowave signal 151′ (at frequency X) containing qubit stateinformation can be sent to a photon detector for measurement/detection.Similarly, to measure qubit 205B, the microwave signal 152′ at frequencyX causes the readout resonator 210B to readout the state information ofqubit 205B, and this microwave signal 152′ (at frequency X) containingqubit state information can be sent to a photon detector formeasurement/detection (or to a heterodyne measurement setup).

The microwave signals 151′ and 152′ can be respectively transmitted fromthe qubit-resonator systems 220A and 220B in transmission or reflection.Although not shown for simplicity, a 4-port circulator (or two 3-portcirculators coupled together through one port) or switch can be placedbetween the qubit-resonator system 220A and the JPC 100, and a 4-portcirculator (or two 3-port circulators coupled together through one port)or switch can be placed between the qubit-resonator system 220B and theJPC 100. In the case of the 4-port circulator/switch, the 4-portcirculator can receive the microwave signal 151 and direct it to the JPC100. Then, the 4-port circulator/switch can receive and direct theentangled microwave signal 151′ to the qubit-resonator system 220A.Finally, the 4-port circulator/switch can receive the microwave signal151′ containing qubit state information from the qubit-resonator system220A and then direct the microwave signal 151′ containing qubit stateinformation to the photon detector (for measurement) or to a heterodynemeasurement setup. The same description applies by analogy to themicrowave signals 152, 152 and qubit-resonator system 220B.

FIG. 3 is a flowchart 300 of a method of configuring a quantum-limitedmicrowave amplifier (e.g., the JPC 100) according to one or moreembodiments. At block 305, a JRM 110 is provided, and at block 310, afirst lumped-element resonator 161 (idler resonator) is connected to theJRM 110 in which the first lumped-element resonator 161 includes one ormore first lumped elements (e.g., capacitors 10A and 10B).

At block 315, a second lumped-element resonator 162 (signal resonator)is connected to the JRM 110 in which the second lumped-element resonator162 includes one or more second lumped elements (e.g., capacitors 10Cand 10D). The JRM 110, the first lumped-element resonator 161, and thesecond-lumped element resonator 162 form a JPC 100. The one or morefirst lumped elements (10A and 10B) and the one or more second lumpedelements (10C and 10D) have a value (e.g., 2C) that is a same, therebyconfiguring the JPC 100 to be spectrally degenerate.

The JRM 110 is a plurality of JJ 130 connected in a loop. The JPCincludes a first port 150A and a second port 150B. The first port 150Ais connected to the first lumped-element resonator 161 via firstcoupling capacitors 20A and 20B. The second port 150B is connected tothe second lumped-element resonator 162 via second coupling capacitors20C and 20D. The first and second coupling capacitors 20A-D have a valueC_(c)/2 which plays a role in determining the bandwidth for the signaland idler resonators 162 and 161.

The first port 150A of the JPC 100 is configured to receive a firstmicrowave signal 151 at a first frequency (e.g., f_(I)=10 GHz) via adifference port Δ of a first hybrid coupler 120A and the second port150B is configured to receive a second microwave signal 152 at a secondfrequency (e.g., f_(S)=10 GHz) via another difference port Δ of a secondhybrid coupler 120B, where the first and second frequencies are the samefrequency (e.g., 10 GHz).

The JPC 100 is configured to amplify the first microwave signal 151 andthe second microwave signal 152 having the same frequency, without thefirst microwave signal 151 leaking out the difference port Δ (signalport) of the second hybrid coupler 120B and without the second microwavesignal 152 leaking out the other difference port Δ (idler port) of thefirst hybrid coupler 120A, because the JPC 100 is configured to bespectrally degenerate. Either the first port 150A or the second port150B is configured to receive input of a pump microwave signal 153 at apump frequency f_(P), in which the pump microwave signal 153 is receivedvia a sum port Σ of either the first hybrid coupler 120A or the secondhybrid coupler 120B. The pump frequency is a sum of the first and secondfrequencies f_(P)=f_(I)+f_(S). The first lumped-element resonator andthe second lumped-element resonator are made of superconductingmaterial.

The first and the second coupling capacitors (20A-D) are lumpedelements, and the lumped elements are selected from the group consistingof gap capacitors, interdigitated capacitors, and/or plate capacitors.

FIG. 4 is a flowchart 400 of a method for configuring a system 200 forremotely entangling qubits through measurement according to one or moreembodiments.

At block 405, a JPC 100 is provided, and at block 410, a firstqubit-resonator system 220A is connected to the JPC 100 in which thefirst qubit-resonator system 220A includes a first qubit 205A coupled toa first readout resonator 210A.

At block 415, a second qubit-resonator system 220B is connected to theJPC 100, in which the second qubit-resonator system 220B includes asecond qubit 205B coupled to a second readout resonator 210B. The JPC100 is configured to remotely entangle the first qubit 205A and thesecond qubit 205B by reading out both the first and the secondcorresponding readout resonators 210A and 210B at the frequency X (e.g.,10 GHz).

The JPC 100 is configured to transmit a first readout signal (e.g.,microwave signal 151′) at the frequency X to the first readout resonator210A in the first qubit-resonator system 220A and transmit a secondreadout signal (e.g., microwave signal 152′) at the frequency X to thesecond readout resonator 210B in the second qubit-resonator system 220B.The photons of the first and the second readout signals 151′ and 152′are entangled at the frequency X by the JPC 100, thereby entangling thefirst qubit 205A and the second qubit 205B coupled respectively to thefirst readout resonator 210A and the second readout resonator 210B whoseresonance frequency is X.

The frequency X is a same value (e.g., 10 GHz) for both the first andthe second readout signals 151′ and 152′. The first and the secondreadout resonators 210A and 210B are each configured with a resonancefrequency equal to the frequency X (e.g., 10 GHz).

Technical benefits include a JPC, and the JPC is configured to generateentangled pairs of photons that propagate on different transmissionlines while the entangled pairs of photons have the same frequency. Thecapability of generating entangled photons which have the same frequencycan be advantageous in certain scenarios such as the following. The JPCcan be utilized for remotely entangling different qubits coupled toreadout resonators where the readout resonators have the same frequency(which simplifies the qubit-resonator design). Generating entangledphotons having the same frequency (i.e., at the signal and idlerresonator frequency) allows for measuring/detecting two-mode squeezingeffects between these entangled photons via wave interference usingpassive unitary beam-splitters such as hybrids. It is noted that twomode squeezing can play important role in quantum communications, andhigh fidelity readout of quantum states. Furthermore, if singlemicrowave photon detectors are used in order to detect these photons,the photon detectors can be identical (i.e., no need for the photondetectors to detect different frequencies). In one or more embodiments,the JPC can be utilized to considerably simplify the integration of twoor more JPCs together on the same chip for example in order to form aquantum-limited directional amplifier.

The term “about” and variations thereof are intended to include thedegree of error associated with measurement of the particular quantitybased upon the equipment available at the time of filing theapplication. For example, “about” can include a range of ±8% or 5%, or2% of a given value.

Aspects of the present invention are described herein with reference toflowchart illustrations and/or block diagrams of methods, apparatus(systems), and computer program products according to embodiments of theinvention. It will be understood that each block of the flowchartillustrations and/or block diagrams, and combinations of blocks in theflowchart illustrations and/or block diagrams, can be implemented bycomputer readable program instructions.

The flowchart and block diagrams in the Figures illustrate thearchitecture, functionality, and operation of possible implementationsof systems, methods, and computer program products according to variousembodiments of the present invention. In this regard, each block in theflowchart or block diagrams can represent a module, segment, or portionof instructions, which includes one or more executable instructions forimplementing the specified logical function(s). In some alternativeimplementations, the functions noted in the block can occur out of theorder noted in the figures. For example, two blocks shown in successioncan, in fact, be executed substantially concurrently, or the blocks cansometimes be executed in the reverse order, depending upon thefunctionality involved. It will also be noted that each block of theblock diagrams and/or flowchart illustration, and combinations of blocksin the block diagrams and/or flowchart illustration, can be implementedby special purpose hardware-based systems that perform the specifiedfunctions or acts or carry out combinations of special purpose hardwareand computer instructions.

The descriptions of the various embodiments of the present inventionhave been presented for purposes of illustration, but are not intendedto be exhaustive or limited to the embodiments discussed herein. Manymodifications and variations will be apparent to those of ordinary skillin the art without departing from the scope and spirit of the describedembodiments. The terminology used herein was chosen to best explain theprinciples of the embodiments, the practical application or technicalimprovement over technologies found in the marketplace, or to enableothers of ordinary skill in the art to understand the embodimentsdiscussed herein.

What is claimed is:
 1. A system for remotely entangling qubits viameasurement, the system comprising: a Josephson parametric converter(JPC); a first qubit-resonator system connected to the JPC, the firstqubit-resonator system including a first qubit coupled to a firstreadout resonator; and a second qubit-resonator system connected to theJPC, the second qubit-resonator system including a second qubit coupledto a second readout resonator, wherein the JPC is configured to remotelyentangle the first qubit and the second qubit by reading out both thefirst and the second readout resonators at a frequency X.
 2. The systemof claim 1, wherein the JPC is configured to transmit a first readoutsignal at the frequency X to the first readout resonator in the firstqubit-resonator system.
 3. The system of claim 2, wherein the JPC isconfigured to transmit a second readout signal at the frequency X to thesecond readout resonator in the second qubit-resonator system.
 4. Thesystem of claim 3, wherein photons of the first and the second readoutsignals are entangled at the frequency X by the JPC, thereby entanglingthe first qubit and the second qubit.
 5. The system of claim 1, whereinthe frequency X is a same value for both the first and the secondreadout signals.
 6. The system of claim 5, wherein the first and thesecond readout resonators are each configured with a resonance frequencyequal to the frequency X.
 7. The system of claim 1, wherein the JPCincludes a Josephson ring modulator (JRM).
 8. The system of claim 7,wherein the JPC includes a first lumped-element resonator connected tothe JRM, the first lumped-element resonator including one or more firstlumped elements.
 9. The system of claim 8, wherein the JPC includes asecond lumped-element resonator connected to the JRM, the secondlumped-element resonator including one or more second lumped elements.10. The system of claim 9, wherein the one or more first lumped elementsand the one or more second lumped elements have a value that is a same,thereby configuring the JPC to be spectrally degenerate.
 11. A method ofconfiguring a system for remotely entangling qubits via measurement, themethod comprising: providing a Josephson parametric converter (JPC);providing a first qubit-resonator system connected to the JPC, the firstqubit-resonator system including a first qubit connected to a firstreadout resonator; and providing a second qubit-resonator systemconnected to the JPC, the second qubit-resonator system including asecond qubit connected to a second readout resonator, wherein the JPC isconfigured to remotely entangle the first qubit and the second qubit byreading out both the first and the second readout resonators at afrequency X.
 12. The method of claim 11, wherein the JPC is configuredto transmit a first readout signal at the frequency X to the firstreadout resonator in the first qubit-resonator system.
 13. The method ofclaim 12, wherein the JPC is configured to transmit a second readoutsignal at the frequency X to the second readout resonator in the secondqubit-resonator system.
 14. The method of claim 13, wherein photons ofthe first and the second readout signals are entangled at the frequencyX by the JPC, thereby entangling the first qubit and the second qubit.15. The method of claim 11, wherein the frequency X is a same value forboth the first and the second readout signals.
 16. The method of claim15, wherein the first and the second readout resonators are eachconfigured with a resonance frequency equal to the frequency X.
 17. Themethod of claim 11, wherein the JPC includes a Josephson ring modulator(JRM).
 18. The method of claim 17, wherein the JPC includes a firstlumped-element resonator connected to the JRM, the first lumped-elementresonator including one or more first lumped elements.
 19. The method ofclaim 18, wherein the JPC includes a second lumped-element resonatorconnected to the JRM, the second lumped-element resonator including oneor more second lumped elements.
 20. The method of claim 19, wherein theone or more first lumped elements and the one or more second lumpedelements have a value that is a same, thereby configuring the JPC to bespectrally degenerate.